Using the conformal field theory approach to the thermoelectric characteristics of fractional quantum Hall states, previously developed in Georgiev (2015) [10] , we show that the thermoelectric power factor of Coulomb-blockaded islands, realized by point contacts in Fabry–Pérot interferometers in the Zk parafermion Hall states, could give reliable signatures for distinguishing the topological orders of different quantum Hall states having identical electric properties. For example, while the conductance peak patterns in the Coulomb blockade regime for such states are practically indistinguishable for vn≪vc even at finite temperature, where vn and vc are the Fermi velocities of the neutral and charged modes respectively, the power factors PT of the corresponding states are much more sensitive to the neutral modes. In particular, the smaller r=vn/vc the bigger the asymmetries in the power factor which combined with the thermal broadening of the conductance peaks due to the neutral modes' multiplicities could give us the ultimate tool to figure out which of the competing quantum Hall universality classes are indeed realized in the experiments. We give a complete description of the power factor profiles in the Z3 and Z4 parafermion states with arbitrary number of quasiparticles localized in the bulk which could be useful for comparison with the experiments.
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